Nonlinear quantum dynamics at a classical second-order resonance

We compare the classical and quantum-mechanical motion of a distribution initially localized on a classical second-order resonance of a driven pendulum. As the driving is increased the quantum state becomes localized about the classically stable region of phase space. The existence of a parity sysmmetry then allows for coherent tunneling between isolated second-order resonances. We compare and contrast the classical and quantum behavior with the aid of perturbation theory.